The optimum linear multiple transmitting and receiving filters are determined for noisy multiple-channel systems using a criterion of minimum output noise variance under the constraints of zero intersymbol interference (ISI) and interchannel interference and of fixed transmitting power. The optimum transmitter appears to generate orthogonal vector functions. For these vector functions the cascade connection of the multiple channel and its multiple matched filter behaves like noninterfering channels (NIC). In the optimum system the ISI is eliminated per NIC by a transversal filter.